Cyclic Elastoplastic Large Displacement Analysis and Stability Evaluation of Steel Tubular Braces

2012 American Transactions on Engineering & Applied Sciences

American Transactions on
Engineering & Applied Sciences

http://TuEngr.com/ATEAS, http://Get.to/Research

Cyclic Elastoplastic Large Displacement Analysis and
Stability Evaluation of Steel Tubular Braces
a*
Iraj H. P. Mamaghani

a
Department of Civil Engineering, School of Engineering and Mines, University of North Dakota, USA.

ARTICLEINFO A B S T RA C T
Article history: This paper deals with the cyclic elastoplastic large
Received 23 August 2011
Accepted 9 January 2012 displacement analysis and stability evaluation of steel tubular braces
Available online subjected to axial tension and compression. The inelastic cyclic
18 January 2012 performance of cold-formed steel braces made of circular hollow
Keywords: sections is examined through finite element analysis using the
Cyclic, commercial computer program ABAQUS. First some of the most
Elastoplastic, important parameters considered in the practical design and ductility
Large displacement,
evaluation of steel braces of tubular sections are presented. Then the
Analysis,
Stability, details of finite element modeling and numerical analysis are
Steel, described. Later the accuracy of the analytical model employed in the
Tubular, analysis is substantiated by comparing the analytical results with the
Brace, available test data in the literature. Finally the effects of some
Finite-Element. important structural and material parameters on cyclic inelastic
behavior of steel tubular braces are discussed and evaluated.

2012 American Transactions on Engineering & Applied Sciences.

1. Introduction
Steel braced frames are one of the most commonly used structural systems because of their
structural efficiency in providing significant lateral strength and stiffness. The steel braces
*Corresponding author (Iraj H.P. Mamaghani). Tel: +1-701-777 3563, Fax: +1-701-777
3782. E-mail address: iraj.mamaghani@engr.und.edu. 2012. American Transactions on
Engineering & Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
75
Online Available at http://TUENGR.COM/ATEAS/V01/75-90.pdf

contribute to seismic energy dissipation by deforming inelastically during an earthquake. The use
of this type of construction indeed avoids the brittle fractures found in beam-to-column
connections in moment-resisting steel frames that occurred in the Northridge earthquake in 1994
and the Kobe earthquake in 1995 (ASCE, 2000; IGNTSDSS , 1996). However, careful design of
steel braced frames is necessary to avoid possible catastrophic failure by brace rupture in the event
of severe seismic loading. The current capacity design procedure adopted in most seismic design
steel specifications (AISC, 1997; CAN-CSA S16.1, 1989), for concentrically braced frames
requires yielding in the braces as primary members, whereas the secondary members of the frame
should remain elastic and hence carry forces induced by the yielding members. The transition from
current perspective seismic codes to performance-based design specifications requires accurate
predictions of inelastic limit states up to structural collapse.

The cyclic behavior of steel brace members is complex due to the influence of various
parameters such as material nonlinearity, structural nonlinearity, boundary condition, and loading
history. The material nonlinearity includes structural steel characteristics such as residual stresses,
yield plateau, strain hardening and Bauschinger effect. The structural nonlinearity includes
parameters such as brace slenderness, cross-section slenderness, width-to-thickness ratio of the
cross-section’s component elements (or radius-to-thickness ratio of circular hollow sections), and
initial out-of-straightness of the brace. This complex behavior results in various physical
phenomena, such as yielding in tension, buckling in compression, postbuckling deterioration of
compressive load capacity, deterioration of axial stiffness with cycling, and low- cycle fatigue
fractures at plastic regions.

Steel braces can be designed to resist only tensile forces, or to resist both tensile and
compressive axial forces. Recent earthquakes and experiments have shown that the
tension-compression braces provide better performance under cyclic loading (during an
earthquake) as compared with the tension-only braces having almost no compressive strength
(IGNTSDSS, 1996). Under severe earthquakes, the braces are subjected to cyclic axial forces and
they are allowed to undergo compression buckling or tensile yield to dissipate the imposed energy
while columns and collector beams respond elastically. Therefore, understanding the behavior of
the bracing members under idealized cyclic loading is an important step in the careful design of
steel braced frames.
76 Iraj H.P. Mamaghani

This paper deals with the inelastic cyclic analysis of steel tubular braces. The most important
parameters considered in the practical design and ductility evaluation of steel braces of tubular
sections are presented. The cyclic performance of steel tubular braces is examined through finite
element analysis using the computer program ABAQUS (2005). The accuracy of the analytical
model employed in the analysis is substantiated by comparing the analytical results with the
available test data in the literature. The effects of some important structural and material
parameters on inelastic cyclic behavior of steel braces are discussed and evaluated.

2. Brace Parameters
Energy absorption through hysteretic damping is one of the great interests in seismic design,
because it can reduce the amplitude of seismic response, and thereby reduce the ductility demand
on the structure. Steel braces are very effective structural members and are widely used as energy
dissipaters in skeletal buildings and offshore structures under extreme loading conditions such as
severe earthquake and wave motion. They also minimize story drift of high-rise buildings for
possible moderate earthquakes during their lifetime.

The most important parameters considered in the practical design and ductility evaluation of
steel braces of tubular sections are section slenderness λ s (Mamaghani, et. al., 1996a, 1996b, 1997;
Mamaghani, 2005, 2008) and slenderness ratio of the member λc (AISC, 1997, 1999). While the
former influences local buckling of the section, the latter controls the overal stability. They are
given by:

1b σy
λs = 3(1 −ν 2 ) ( for box sec tion ) (1)
π t E

d σ
λs = 3(1 −ν 2 ) y ( for circular sec tion ) (2)
2t E

1 KL σ y
λc = (3)
π r E

77

where, b = flange width of a box section; t = plate thickness of the cross-section elements;
σ y = measured yield stress; E = Young’s modulus; ν = Poisson’s ratio; d = outer diameter of

the circular section; K = effective length factor; L = measured length of the brace; and r= radius
of gyration of the cross section. It is worth noting that the section slenderness, λ s , represents the
width-thickness ratio parameter of the flange plate for a box section and the diameter-thickness
ratio of a circular hollow section for a given material.

The limiting diameter-thickness ratio specified in AISC (1997) for plastic design of circular
hollow sections is d / t = 0.045 E / σ y . This d / t limit can be converted to a limiting slenderness

parameter for a compact element according to Equation 2. The corresponding value of λ s ,
considering υ = 0.3 for structural steels, is:

0.045 E σy
λs = 3(1 − 0.32 ) = 0.037 (4)
2σ y E

This implies that when λs ≤ 0.037 , no local buckling occurs before the cross-section attains
full plastic capacity. The limiting width-thickness ratio specified in AISC (1997) for
non-compact circular hollow sections is d / t = 0.11E / σ y which corresponds to λ s = 0.09 .

The ductility behavior of the circular hollow section braces is significantly sensitive to λ s when it
is less than 0.09. The maximum member slenderness limits specified in AISC (1997) for
special concentrically braced frames (SCBF) and ordinary concentrically braced frames are
λ c = 1.87 ( KL / r ≤ 1000 / σ y ) and λc = 1.35 ( KL / r ≤ 720 / σ y ), respectively. SCBF are

expected to withstand significant inelastic deformation when subjected to the force resulting from
the motion of the design earthquake. SCBF have increased ductility due to lesser strength
degradation when compression braces buckle.

3. Numerical Method
Steel braces are vulnerable to damage caused by local and overall interaction buckling during
a major earthquake. A sound understanding of the inelastic behavior of steel braces is important in
developing a rational seismic design methodology and ductility evaluation of steel braced frame
structures.

An accurate cyclic analysis of braced frames requires precise methods to predict the cyclic
inelastic large-deflection response of the braces. This has been a subject of intensive research and
a variety of analytical methods have been developed to simulate the hysteretic behavior of braces
over the past few decades. The main research approaches used for the cyclic analysis of braces may
be classified as: (1) empirical models, (2) plastic-hinge models, and (3) elastoplastic finite element
models (Mamaghani et al., 1996a). The more accurate models were based on the finite element
method considering geometric and material nonlinearities. This method is generally applicable to
many types of problems, and it requires only the member geometry and material properties
(constitutive law) to be defined.

3.1 Finite Element Method
The finite element analysis is carried out by using the commercial computer program
ABAQUS. The shell element S4R is used in modeling the brace member (ABAQUS, 2005). The
S4R element is a three-dimensional, double-curved, four-node shell element with six degrees of
freedom per node that uses bilinear interpolation. Because the S4R element contains only one
sample point while five layers are assumed across the thickness, the spread of plasticity is
considered through both the thickness and plane of the element. This shell element, which uses
reduced integration, is applicable to both thin and thick shells, and can be used for finite strain
applications.

In the analysis, both material and geometrical nonlinearities are considered. For large
displacement analysis, the elements are formulated in the current configuration, using current
nodal positions. Elements therefore distort from their original shapes as the deformation increases.
The stiffness matrix of the element is obtained from the variational principle of virtual work. The
modified Newton-Raphson iteration technique coupled with the displacement control method is
used in the analysis (Zienkiewicz, 1977). The displacement convergence criterion is adopted and
the convergence tolerance is taken as 10-5. The details of elastoplastic large-displacement
formulation and solution scheme are reported in the work by the author (Mamaghani, 1996).

79

3.2 Analytical Modeling
A series of numerical studies on the cyclic behavior of steel braces are carried out using the
numerical finite element method described in the previous section, and the results are compared
with the experiments. The results for three typical examples, S7A, S7B, and S7C (Elchalakani et
al., 2003), presented hereafter are intended to verify the accuracy of the numerical method. These
specimens are subjected to three loading histories in order to better understand the cyclic behavior
of cold-formed circular hollow-section braces. The details of the test can be found in Elchalakani et
al. ( 2003).

Figure 1: Analyzed circular hollow section steel brace and initial imperfection.

Table 1: Properties of the analyzed braces.
Test Number Specimen Shape Ag (mm2) L (mm) λs λc δ y (mm) Py (kN)
S7A CHS 139.7x3.5 1498 2820 0.06 0.4 5.34 568
S7B CHS 139.7x3.5 1498 2820 0.06 0.4 5.34 568
S7C CHS 139.7x3.5 1498 2820 0.06 0.4 5.34 568

The shape and dimensions of the analyzed braces are given in Table 1. For comparison, the
selected brace parameters ( λc = 0.4 and λs = 0.06 ) are kept the same. These parameters represent
a non-compact member having inelastic behavior. The analyzed fixed-end tubular braces subjected
to cyclic concentric axial loading are modeled as shown in the Figure 1. An initial imperfection of

⎛ πx ⎞
γ x = γ 0 sin ⎜ ⎟ (5)
⎝ L ⎠

is assumed in the analysis, where the initial deflection at midspan of the member γ 0 is taken as the
measured value of L/3160 during the test.


Figure 2: Tri-linear stress-strain model for steel.

3.3 Material Model
The analyzed cold-formed circular hollow sections are AS 1163 grade C350L0 (equivalent to
ASTM A500 tubes) with the yield stress of σ y = 379 MPa and the ultimate tensile strength of

σ u = 451 MPa. In the analysis, the material nonlinearity is accounted for by using the kinematic
hardening rule. Figure 2 shows the tri-linear stress-strain material model adopted in the analysis.
The Young modulus of elasticity of the steel is assumed to be E = 200 GPa. The strain hardening
modulus is assumed to be 2 percent of the initial Young modulus ( E st = 0.02 E ).

Figure 3: Meshing details and boundary conditions.

81

3.4 Cyclic Loading History
In the analysis three cyclic loading histories are applied. The first loading history is a large
compression-tension monocycle with a maximum normalized displacement amplitude
m = δ max / δ y , where δ m ax is the maximum displacement in the compression-half cycle at load

reversal and δ y = ε y L = Py L / EA is the yield displacement corresponding to the squash load of cross

section Py = σ y A (A = area of the cross-section; σ y = yield stress; L= the length of the brace). The

large amplitude used in the monocycle is applied to examine the inelastic response of the brace
when subjected to a very large seismic demand during a possible near-field excitation (Krawinkler
et al., 2000). The second loading history is a uniform increase of displacement amplitude up to
failure with the maximum normalized displacement amplitudes of m = 1, 2, 3, …, where each
amplitude is repeated only once. In the third loading history, a uniform increase of the
displacement is used similar to the second loading history except that the oscillations are repeated
three times at each amplitude ( m = 1, 2, 3, …, etc.).

3.5 Finite Element Meshing and Boundary Conditions
The details of the finite-element meshing pattern adopted in the analysis of hollow circular
sections are shown in Figure 3. The brace is subdivided into a total number of 2100 shell elements
(70 elements along the brace length and 30 elements in the circumferential direction). A finer mesh
pattern is used at the center and the ends of the brace, where large deformation is expected, as
shown in Figure 3. In the analysis, the left end of the brace is fully fixed and the right end is
modeled as a guided support to apply axial displacement, as shown in Figure 3. The axial load, P,
and vertical deflection at midspan, V, are obtained from analysis.

4. Numerical Results

4.1 Example 1
The first example is concerned with the analysis of the brace S7A, which has a nominal length
of 2820 mm, a member slenderness parameter of λc = 0.4 and a section slenderness of λs = 0.06
(Table 1). These parameters represent a non-compact member having inelastic behavior.

This brace is subjected to a large compression-tension monocycle with maximum normalized
displacement amplitude of m = 18.24 (the first loading history) to examine the inelastic response of

the brace under a very large seismic demand. This value is larger than the upper limit for m = 10 ,
which is likely to occur in a near-source excitation (Krawinkler et al., 2000). In order to check the
effects of mesh density and loading increment (loading time steps) on the inealstic cyclic behavior
of the brace, three analyses are carried out on this brace. The first analysis, designated as the
original analysis, uses the original meshing pattern shown in Figure 3 with a total number of 2100
shell elements. The second analysis, designated as the mesh-increment analysis, uses a finer mesh
density at the central segment and at the ends of the brace by doubling the mesh number in these
regions with a total number of 3300 shell elements. The third analysis, designated as the
step-increment analysis, utilizes the original meshing but doubling the time step by reducing the
displacement increment to half of that used in the original analysis. Figures 4a and 4b compare the
normalized axial load P / Py -axial deformation δ / δ y hysteresis loop obtained from the

experiment and analyses. With reference to these figures, the following observations can be made:
1. The initial stiffness and buckling load capacity are slightly lower in the experiment than
those predicted by the analyses using various mesh sizes and loading incremens. This may
be due to the experimental boundary conditions (unavoidable rotation at the fix-ends) and
the assumed initial imperfection in the analysis. In the analysis the cross-section
out-of-straightness and residual stress are not accounted for. It is worth noting that the
previous research by the author indicates that the initial residual stresses and initial section
imperfections significantly decrease the initial stiffness and initial buckling load capacity
and have almost no effect on the subsequent cyclic behavior of the member (Mamaghani et
al., 1996a, Banno et al., 1998).
2. Under compressive load, the overall buckling was followed by local buckling at the center
and brace ends. From Figures 4a and 4b, it can be observed that the overall shape of the
predicted hysteresis loop is significantly closer to the experiment.
3. Under tension load, the behavior of the brace is well predicted up to δ / δ y = 9.3 , where there

is a sharp decrease in predicted tensile strength beyond this displacement. The observed
discrepancy between experimental and analytical results when the specimen is stretched
beyond δ / δ y = 9.3 might be due to the formation of a plastic hinge at the member

midspan under combined biaxial hoop stress and axial stress. By further stretching the

83

member, the spread of plasticity fully covered the whole cross section at midspan and
extended on both sides of this section, leading to the reduction of load carrying capacity,
see Figure 5.

1.5

1.5

1
1

0.5
0.5

0
0 -20 -10 0 10 20
-20 -10 0 10 20
-0.5 δ/δy
-0.5 δ/δy
Original analysis
-1 Step-increased
-1
Test Mesh-increased

P/Py
P/Py

Analysis -1.5 Test
-1.5

(a) Axial load versus axial displacement. (b) Effects of mesh density and load steps.

1.5 1.5
S7A

1
1

0.5
0.5

0
0
-400 -300 -200 -100 0 100
-50 -40 -30 -20 -10 0 10
v (mm) -0.5
Local buckling -0.5
progress (mm)
Node 1088 -1
Node 1104 -1
P/Py

-1.5
P/Py

-1.5

(c) Deflection at the top face (Node 1088) (d) Local buckling progress at midspan
and bottom face (Node 1104) of the
cross-section at midspan.

Figure 4: Comparison between experimental and predicted hysteretic loop for brace S7A.

4. The results in Figure 4(b) show that the increase in time step and use of fine mesh do not
have significant effects on the overall predicted behavior except for a slight improvement in
postbuckling behavior where the predicted results closely fit the test results. Under tensile
loading beyond the δ / δ y = 9.3 , the predicted tensile load capacity drops slightly earlier


for the analysis using fine mesh as compared with the other analyses. This is because the
spread of plasticity and formation of the plastic hinge takes place faster for the fine mesh
model.

Figure 4(c) shows normalized axial load P / Py versus vertical deflection V, at the top face
(Node 1088) and bottom face (Node 1104) of the cross-section at the midspan of the member
(Figure 3), obtained from the analysis. The results in this figure show that the relative vertical
deflection at the top and bottom faces of the cross-section at midspan increases as the member
undergoes large axial deformation. The difference between the vertical displacements of the top
face and bottom face at midspan indicates the progress of local buckling, which is plotted in Figure
4(d). Figure 5 shows the deformation of the specimen at the end of compression load and tension
stretching. Under compression load, the overall buckling was followed by local buckling at the
center and brace ends. A smooth kink formed at midspan of the brace under compression load. A
semi-elephant-foot (an outward folding mechanism) was formed at the fixed ends of the brace, as
shown in Figure 5. During the tensile stretching, the brace suffered excessive stretching at the
midspan because of the development of a plastic hinge caused by a very large accumulation in local
deformation. This represents a tear-through-failure mode, as the specimen exhibited during the test
(Elchalakani et al., 2003). These observed behaviors under compression and tension loads are
reflected in the normalized load-displacement hysteretic loop shown in Figure 4.

4.2 Example 2
The second example is concerned with the analysis of the brace S7B, which has a nominal
length of 2820 mm, a member slenderness of λc = 0.4 and a section slenderness of λ s = 0.06 (Table
1). This brace is subjected to a uniform increase of displacement amplitude up to failure with the
maximum normalized displacement amplitudes of m = 1, 2, 3, …, where each amplitude is
repeated only once (the second loading history). The original meshing pattern shown in Figure 3,
with a total number of 2100 shell elements, is utilized in the analysis.

85

Figure 5: Deformed configuration of brace S7A at the final stage of compression and tension cyclic
loading.

Figure 6(a) compares the normalized axial load P / Py -axial deformation δ / δ y hysteresis
loops obtained from the experiment and analysis. Figure 6(b) shows the normalized axial load
P / Py versus vertical deflection V, at the midspan of the member (Figure 3), obtained from the

analysis. Comparison between hysteresis loops in Figure 6(a) shows that there is a relatively good
agreement between analytical results and experiments. An observed small discrepancy between
experimental and analytical hysteresis loops is that the predicted cyclic load capacities in
compression direction of loading are slightly higher than those of the experiment. The possible
reasons are: (a) the tri-linear kinematic hardening rule adopted in the analysis does not accurately
consider the reduction of the elastic range due to plastic deformation (Bauschinger effect). In this
model the size of the elastic range is taken to be constant which does not represent the actual
behavior of structural steel (Mamaghani et al. 1995; Shen et al., 1995). More accurate results can
be obtained from analysis using a cyclic constitutive law representing the more realistic behavior of
the material; (b) the brace fixed-end boundary conditions may have shown some degree of
flexibility during the tests, which is not considered in the analysis; and (c) in the analysis the
cross-section’s out of straighness and residual stresses, which affect the initial buckling load, are
not considered.


1.5

1 1.5

0.5 1

0.5
0
-8 -4 0 4 8

δ/δy 0
-0.5 -200 -150 -100 -50 0

V (mm)
-0.5

-1
Test
-1

P/Py
Analysis

P/Py
-1.5 Analysi
-1.5

(a) (b)

Figure 6: Comparison between experimental and predicted hysteretic loop for brace S7B.

Figure 6(b) shows that there is a residual midspan deflection at the end of tensioning in each
cycle. The residual deflection of the brace at the end of the previous tensioning has a large effect
on the buckling capacity and subsequent cyclic behavior. Figure 6(b) shows the progress of
residual midspan deflection due to cycling obtained from analysis. In spite of large progress in
buckling, the buckling load does not decrease significantly due to cyclic strain hardening.

4.3 Example 3
The third example is concerned with the analysis of the brace S7C, which has a nominal length
of 2820 mm, a member slenderness of λ c = 0.4 and a section slenderness of λs = 0.06 (Table 1).
This brace is subjected to a uniform increase in displacement amplitude up to failure with the
maximum normalized displacement amplitudes of m = 1, 2, 3, …, where each amplitude is
repeated three times (the third loading history). The original meshing pattern as shown in Figure 3,
with a total number of 2100 shell elements, is utilized in the analysis.

Figure 7(a) compares the normalized axial load P / P -axial deformation δ / δ y hysteresis loop
y

obtained from experiment and analysis. Figure 7(b) shows the normalized axial load P / Py versus
vertical deflection V, at the midspan of the member (Figure 3), obtained from the analysis.
Comparison between hysteresis loops in Figure 7(a) shows there is a relatively good agreement
87

between analytical results and experiments. These results indicate that the numerical method and
finite element modeling employed in the numerical analysis can predict with a reasonable degree of
accuracy the experimentally observed cyclic behavior of axially loaded fixed-end steel braces of
circular hollow sections.

1.5

1.5

1
1

0.5
0.5

0
-8 -4 0 4 8 0
-200 -150 -100 -50 0
δ/δy
-0.5
V (mm) -0.5

-1 Test
-1
Analysis
P/Py

P/Py
-1.5 Analysis
-1.5

(a) (b)

Figure 7: Comparison between experimental and predicted hysteretic loop for brace S7C.

5. Conclusions
This paper dealt with the inelastic cyclic elastoplastic finite-element analysis and stability
(strength and ductility) evaluation of steel tubular braces subjected to axial tension and
compression. The most important parameters considered in the practical seismic design and
ductility evaluation of steel braces of tubular sections, such as brace slenderness, cross-section
slenderness, material behavior, and loading history, were presented. The elastoplastic cyclic
performance of cold-formed steel braces of circular hollow sections was examined through
finite-element analysis using the commercial computer program ABAQUS and employing a
tri-linear kinematic strain hardening model to account for material nonlinearity. The details of
finite element modeling and numerical analysis were described. The accuracy of the analytical
model employed in the analysis was substantiated by comparing the analytical results with the
available test data in the literature. The effects of some important structural, material, and loading
history parameters on cyclic inelastic behavior of steel braces were discussed and evaluated with
reference to the experimental and analytical results. It has been shown that the numerical method
and finite element modeling employed in the numerical analysis can predict with a reasonable


degree of accuracy the experimentally observed cyclic behavior of axially loaded fixed-end steel
braces of circular hollow sections.

6. References
ABAQUS / Standard User’s Manual. (2005). Ver. 6.5, Hibbitt, Karlsson and Sorensen, Inc.

Amrican Institute of Steel Constructions (AISC-LRFD). (1999). Load and resistance factor design
specification for structural steel buildings, 3rd Edition, Chicago.

Amrican Institute of Steel Constructions (AISC). (1997). Seismic provisions for structural steel

buildings, Chicago, Illinois.
ASCE. (2000). Steel moment frames after Northridge. J. Struct. Eng., 126(1) (special issue).

Banno, S., Mamaghani, I. H.P., Usami, T., and Mizuno, E. (1998). Cyclic elastoplastic large
deflection analysis of thin steel plates. Journal of Engineering Mechanics, ASCE,
USA,Vol. 124, No. 4, pp. 363-370.

Canadian Standards Associations (CAN-CSA S16.1). (1989). Steel structures for buildings, limit

state design.
Elchalakani, M., Zhao, X. L., Grzebieta, R. (2003). Test of cold-formed circular tubular braces
under cyclic axial loading. J. of Struct. Eng., ASCE, 129(4), pp. 507-514.

Interim Guidelines and New Technologies for Seismic Design of Steel Structures (IGNTSDSS).

(1996). In T., Usami (eds), Committee on New Technology for Steel Structures,
Japan Society of Civil Engineers (JSCE), Japan,(in Japanese).
Krawinkler, R., Akshay, G., Medina, R., and Luco, M. (2000). Development of loading histories
for testing of steel-to-beam assemblies. Report prepared for SAC Steel Project, Dept. of
Civil and Environmental Engineering, Stanford University.

Mamaghani, I.H.P. (2008). Seismic Design and Ductility Evaluation of Thin-Walled Steel Bridge
Piers of Box Sections, Transportation Research Record: Journal of the Transportation
Research Board, Volume 2050, pp. 137-142.

Mamaghani, I.H.P. (2005). Seismic performance evaluation of thin-walled steel tubular columns,
Structural Stability, Structural Stability Research Council, Montreal, Quebec, Canada,
pp.1-10.

Mamaghani, I.H.P. (1996). Cyclic elastoplastic behavior of steel structures: theory and
experiments. Doctoral Dissertation, Department of Civil Engineering, Nagoya University,
89

Nagoya, Japan.

Mamaghani, I.H.P., Usami, T., and Mizuno, E. (1996a). Inelastic large deflection analysis of
structural steel members under cyclic loading. Engineering Structures, UK, Elsevier
Science, 18(9), pp. 659-668.

Mamaghani, I.H.P., Usami, T., and Mizuno, E. (1996b). Cyclic elastoplastic large displacement
behavior of steel compression members. Journal of Structural Engineering, JSCE, Japan,
Vol. 42A, pp. 135-145.

Mamaghani, I.H.P., Usami, T., and Mizuno, E. (1997). Hysteretic behavior of compact steel box
beam- columns. Journal of Structural Engineering, JSCE, Japan, Vol. 43A, pp. 187-194.

Mamaghani, I.H.P., Shen, C., Mizuno, E., and Usami, T. (1995). Cyclic behavior of structural
steels. I: experiments. Journal of Engineering Mechanics, ASCE, USA, Vol.121, No.11,
pp. 1158-1164.

Shen, C., Mamaghani, I.H.P., Mizuno, E.,and Usami, T. (1995). Cyclic behavior of structural
steels. II: theory. Journal of Engineering Mechanics, ASCE, USA, Vol.121, No.11, pp.
1165-1172.

Zienkiewicz, O.C. (1977). The finite element method. 3rd Ed., McGraw-Hill, New York.

Iraj H.P. Mamaghani is an Associate Professor of Civil Engineering at University of North
Dakota. He received his B.Sc. in Civil Engineering from Istanbul Technical University with
Honors in 1989. He continued his Master and PhD studies at University of Nagoya, Japan, where
he obtained his Master and Doctor of Engineering degrees in Civil Engineering. Dr. Mamaghani
has published several papers in professional journals and in conference proceedings. Dr.
Mamaghani works in the area of civil engineering, with emphasis on structural mechanics and
structural engineering. He focuses on cyclic elastoplastic material modeling, structural stability,
seismic design, advanced finite element analysis and ductility evaluation of steel and composite
(concrete-filled steel tubular) structures.

Peer Review: This article has been internationally peer-reviewed and accepted for publication
according to the guidelines given at the journal’s website.


Cyclic Elastoplastic Large Displacement Analysis and Stability Evaluation of Steel Tubular Braces

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